The position of a particle is given by $x ( t ) = 23 t - 1.2 t ^ { 3 }$ , where x(t) is in meters and t is in seconds. The (positive) time when the particle has zero velocity is
A) 1.2 seconds.
B) 2.5 seconds.
C) 2.3 seconds.
D) 23 seconds.

Question

Quizplus · Accepted Answer

The velocity is the derivative of the position function: $v(t) = \frac{d}{dt}(23t - 1.2t^3) = 23 - 3.6t^2$. Setting $v(t) = 0$ gives $23 - 3.6t^2 = 0$. Solving for $t$, we get $t^2 = \frac{23}{3.6}$, so $t = \sqrt{\frac{23}{3.6}} \approx 2.5$ seconds.

The Position of a Particle Is Given By x(t)=23t−1.2t3x ( t ) = 23 t - 1.2 t ^ { 3 }x(t)=23t−1.2t3

The Position of a Particle Is Given By $x ( t ) = 23 t - 1.2 t ^ { 3 }$